How did they calculate what T does to the elements of B?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 20EQ
icon
Related questions
Question
100%

How did they calculate what T does to the elements of B?

Example 10.6 Let T : P3 (R) → M2×2 (R) be the linear transformation defined
via
T (ax³ + bx² + cx + d)
Consider the bases B = (1, x, x², x³) and
=
C
- (( ) ( ) ( ) ( ))
2
>
"
T(x²) =
(18)
a + d b
b+c a-d,
C
-a).
0
TM)= (19), 7() = (1 -
(1)
T(x)
0
0
(19)
2
of P3 (R) and M2×2 (R), respectively. Find the matrix representation of T with
respect to the bases B and C.
First, we need to know what T does to the elements of B:
T(x³) =
(234)
(235)
(236)
Transcribed Image Text:Example 10.6 Let T : P3 (R) → M2×2 (R) be the linear transformation defined via T (ax³ + bx² + cx + d) Consider the bases B = (1, x, x², x³) and = C - (( ) ( ) ( ) ( )) 2 > " T(x²) = (18) a + d b b+c a-d, C -a). 0 TM)= (19), 7() = (1 - (1) T(x) 0 0 (19) 2 of P3 (R) and M2×2 (R), respectively. Find the matrix representation of T with respect to the bases B and C. First, we need to know what T does to the elements of B: T(x³) = (234) (235) (236)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax